Distribute or factor

Front

What does it mean to distribute in algebra?

Back

To distribute means to multiply a term by each term inside a set of parentheses. For example, in the expression a(b + c), you would calculate ab + ac.

Front

What is the formula for finding the Greatest Common Factor (GCF) of two numbers?

Back

The GCF of two numbers is the largest number that divides both of them without leaving a remainder. It can be found using prime factorization or the Euclidean algorithm.

Front

How do you find the GCF of 64xy and 72xyz?

Back

First, find the prime factorization of both numbers: 64 = 2^6, 72 = 2^3 * 3^2. The GCF is found by taking the lowest power of each common prime factor: GCF = 2^3 = 8, and since both terms have 'xy', the GCF is 8xy.

Front

What is the result of distributing -3 over (m + 4)?

Back

The result is -3m - 12, as you multiply -3 by both m and 4.

Front

What is the process of factoring an expression?

Back

Factoring an expression involves rewriting it as a product of its factors. For example, 10m + 64 can be factored as 2(5m + 32).

Front

What is the distributive property?

Back

The distributive property states that a(b + c) = ab + ac. It allows you to multiply a single term by each term in a sum or difference.

Front

How do you factor the expression 10m + 64?

Back

To factor 10m + 64, find the GCF of the coefficients (10 and 64), which is 2. Then, factor out 2: 10m + 64 = 2(5m + 32).

Front

What is the GCF of 14m and 49mn?

Back

The GCF is 7m, as 14 = 2 * 7 and 49 = 7^2, and both terms share the factor 7 and the variable m.

Front

What is the first step in distributing an expression?

Back

The first step is to identify the term outside the parentheses and the terms inside the parentheses that need to be multiplied.

Front

Can you give an example of a situation where you would need to use the GCF?

Back

You would use the GCF when simplifying fractions, finding common denominators, or factoring polynomials.